Topological Anderson insulating phases in the long-range Su-Schrieffer-Heeger model

Hsu, Han Lin; Chen, Tsung-Wei

doi:10.1103/physrevb.102.205425

Cited by 39 publications

(25 citation statements)

References 27 publications

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“…This will allow for a comparison between that operator with the new one associated with a new chiral symmetry, see Section IV. Note that the extended SSH has been addressed in the past in several works [10][11][12][13][14][15][16][17][18][19][20][21], but as far as we know its indexation problem has never been discussed.…”

Section: Modelmentioning

confidence: 99%

“…This will be expected in particular if a band inversion occurs in the band structure of the linear chain as the relative values of the hopping terms change. In order to illustrate the previous arguments, we consider in this paper the chiral symmetry protected * rdias@ua.pt topological SSH insulator and add to it long-range hopping terms [10][11][12][13][14][15][16][17][18][19][20][21] in such a way that the Hamiltonian eigenbasis remains the same and the usual SSH chiral operator remains a mapping operator between eigenstates of the Hamiltonian (allowing us to compare it with new chiral operators). This model is simply the extended SSH chain with next-nearest neighbor (NNN) hoppings.…”

Section: Introductionmentioning

confidence: 99%

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Long-range hopping and indexing assumption in one-dimensional topological insulators

Dias,

Marques

2021

Preprint

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In this paper, we show that the introduction of long-range hoppings in 1D topological insulator models implies that different possibilities of site indexation must be considered when determining the bulk topological invariants in order to avoid the existence of hidden symmetries. The particular case of the extended SSH chain is addressed as an example where such behavior occurs. In this model, the introduction of long-range hopping terms breaks the bipartite property and a band inversion occurs in the band structure as the relative values of the hopping terms change, signaling a crossover between hopping parameter regions of "influence" of different chiral symmetries. Furthermore, edge states become a linear combination of edge-like states with different localization lengths and reflect the gradual transition between these different chiral symmetries.

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Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Long-range hopping and indexing assumption in one-dimensional topological insulators

Dias,

Marques

2021

Preprint

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“…A significant interest is attracted by generalizations of SSH model. They include extensions on two-chain ladders [13], 2D lattice [14], and long-range hopping [15]. This model has a deep connection to driven-dissipative systems described by non-Hermitian Hamiltonians [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings

Shapiro,

Remizov,

Lebedev

et al. 2021

Preprint

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A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of 1D system with a non-trivial band topology. An interplay of disorder and topological ordering in the SSH model is of a great interest owing to experimental advancements in synthesized quantum simulators. In this work, we investigate a special sort of a disorder when inter-cell hopping amplitudes are random. Using a definition for Z2-topological invariant ν ∈ {0; 1} in terms of a non-Hermitian part of the total Hamiltonian, we calculate ν averaged by random realizations. This allows to find (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite size fluctuations of ν for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green function method for a thermodynamic limit.

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“…Several extensions of the SSH model have been provided by some authors. For example, one of these extensions is the introduction of the longer-range hoppings [7][8][9][10][11] . These longer-range hoppings can be classified into two distinct classes.…”

Section: Introductionmentioning

confidence: 99%

Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings

Du,

Li,

et al. 2021

Preprint

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For the Su-Schrieffer-Heeger (SSH) model on the two-dimensional square lattice, two third nearest neighbor hoppings which preserve chiral symmetry are introduced. Like the case of one dimension, the longer-range hopping can drive topological transitions and leads to the larger topological invariant (vectored Berry phase for the two dimensional SSH model). We obtain the phase boundaries and topological phase diagrams from the winding pattern of ρ(k l ) of the Bloch Hamiltonian. Effects of correlations on the extended two dimensional SSH model are also investigated. The correlation shifts the phase boundaries and leads to topological transitions. Several special points in non-interacting phase diagrams are chosen to illustrate the different phase transitions and a correlations-driven topologically non-trivial phase from the trivial one is found. In this work, the slave-rotor mean field method is applied to the interacting model and we focus on the case of physical electrons, i.e. the Mott transition of charge degree of freedom is avoided in our investigations.

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Topological Anderson insulating phases in the long-range Su-Schrieffer-Heeger model

Cited by 39 publications

References 27 publications

Long-range hopping and indexing assumption in one-dimensional topological insulators

Long-range hopping and indexing assumption in one-dimensional topological insulators

Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings

Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings

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